The present invention relates to an equalizer for equalizing the waveform of a received signal with a transversal filter having variable tap gains and, more particularly, to an automatic equalizer for automatically removing linear distortions caused in a transmission system by using a waveform of a predetermined shape which is periodically present in the received signal.
The automatic equalizer may be applied to a ghost canceller of a television receiver set. FIG. 1 shows a known ghost canceller using a transversal filter whose tap gains are variable. The leading edge of the first vertical synchronizing pulse in the vertical blanking period of a video signal is used as a reference signal for ghost detection ("Digitized Automatic Ghost Canceller" by Murakami et al; Electronic Communication Committee Technical Research Report EMC J 78-37, November, 1978).
In FIG. 1, reference numeral 20 represents the transversal filter whose tap gains are variable and which comprises a tapped delay line 21, weighting circuits 22, and an adder circuit 23. The delay time T between adjacent taps of tapped delay line 21 is selected to have a value smaller than the reciprocal of two times the highest frequency of the input video signal, e.g. 0.1 .mu.S. The total number of taps depends upon the range of delay (or lead) time of the ghost to be cancelled. Providing that the total number of taps is 100, a time range of 10 .mu.S can be covered.
A tap set to have a maximum weighting value (tap gain) is called the main tap. Taps whose delay time is shorter than that of the main tap are called forward taps, while taps whose delay time is longer are called backward taps. Providing that the 20th tap of 100 taps is selected as the main tap, up-to-2 .mu.S leading ghosts and up-to-8 .mu.S delayed ghosts can be cancelled out. The weighting circuit 22 connected to each of taps is a multiplier whose multiplying coefficient denotes the tap gain. It is assumed that the tap gain of the main tap is represented by c.sub.0, the tap gains of the forward taps are represented by c.sub.-M -c.sub.-1, and the tap gains of the backward taps are represented by c.sub.1 -c.sub.N. c.sub.0 has a value of about 1 usually, and the values of the other tap gains c.sub.i (i=-M-N) are smaller than c.sub.0 in absolute value.
With such a transversal filter, a ghost component (including a waveform distortion caused by a filter or the like) which is present at an input terminal 10 can be substantially cancelled out at an output terminal 30 if the tap gains {c.sub.i } (a series of c.sub.-M -c.sub.0 -c.sub.N) are set to have respective appropriate values. The automatic control of the tap gains to minimize the ghost component at the output may be performed as follows.
An input video signal applied to input terminal 10 is supplied to an input waveform memory 41 through a differentiation circuit 40. This input waveform memory 41 extracts and stores, under the control of a timing circuit 44 responsive to the input video signal, only the signal component having a predetermined length of the leading edge of the vertical synchronizing pulse adapted to detect ghost component.
A reference waveform generator circuit 45 is provided which responds to timing circuit 44 to generate a distortion-free reference waveform of the signal component at the leading edge of the vertical synchronizing pulse. An output video signal of output terminal 30 is applied to a subtracter circuit 43 through a differentiation circuit 42. This subtracter circuit 43 provides the difference between output signals of differentiation circuit 42 and reference waveform generator circuit 45. The difference signal is applied to an error waveform memory 46 which is responsive to timing circuit 44 to extract an error (distortion) waveform of the signal component at the leading edge of the vertical synchronizing pulse from the output signal of subtractor circuit 43, and memorize the error waveform.
The waveform thus memorized in input waveform memory 41 is represented by {x.sub.k } as a series of sampled values at an interval of 0.1 .mu.S equal to the tap interval of transversal filter 20. Similarly, the output waveform of differentiation circuit 42 is represented by {y.sub.k }; the reference waveform generated by reference waveform generator circuit 45 is represented by {r.sub.k }; and the error waveform from subtractor circuit 43 is represented by {e.sub.k } (e.sub.k =Y.sub.k -r.sub.k).
{x.sub.k-i } and {e.sub.k } are read out from respective memories 41 and 46 by a clock signal to perform a correlation operation represented by ##EQU1## The correlation range [P, Q] is usually taken from P=-2M to Q=2N. The physical meaning of d.sub.i represents the approximate magnitude of a ghost with a delay time iT (T is the tap interval).
The tap gain {c.sub.i } is stored in a tap gain memory 48. The initial values of tap gains are: c.sub.0 =1; c.sub.-M .about.c.sub.-1 =0; and c.sub.1 .about.c.sub.N =0. Every time the operation of equation (1) is finished with respect to i (-M.about.N) the tap gain c.sub.i is read out from tap gain memory 48, and is subjected to a correction, which is represented by: EQU c.sub.i, new =c.sub.i, old -ad.sub.i ( 2)
wherein a has a small positive value. After the correction, the tap gain is rewritten in tap gain memory 48. The operations represented by equations (1) and (2) are conducted during one field period with respect to all taps by a tap gain correction circuit 47.
The operations are repeated every time the reference waveform is received (or once per one field).
As a result, the error waveform {e.sub.k } gradually approaches 0. Namely, the output waveform {y.sub.k } approaches the reference waveform {r.sub.k }. {c.sub.i } is finally converged to have a value {c.sub.i }.sub.opt, and the output waveform {y.sub.k } is corrected to have the smallest margin of error, as defined by: ##EQU2## (see the above-cited literature).
When tap gain correction is repeated using equations (1) and (2), the tap gain value is converged to have {c.sub.i }.sub.opt in principle. Because the frequency response of transversal filter 20 is not ideal, the tap gain value is not necessarily actually converged to {c.sub.i }.sub.opt. {c.sub.i } changes toward {c.sub.i }.sub.opt for a certain initial time period after the start of successive correction control, but as time passes, it happens that {c.sub.i } diverges gradually.
There is also known a method of correcting tap gain by: EQU c.sub.i, new =c.sub.i, old -a e.sub.i ( 4)
instead of by equations (1) and (2) to simplify the tap gain correction circuit. This is called the zero-forcing method. In the zero-forcing method, {c.sub.i } may diverge in principle depending upon the shape of the input waveform {x.sub.k }, even if the frequency response to transversal filter is ideal.
For the purpose of avoiding the above-mentioned divergence of the tap gain correction control, the following modification of equation (2) (similarly in the case of equation (4)) is carried out so as to provide a small leak to the tap gain correction control: ##EQU3## wherein .beta. and l represent small positive values for the leak, and sgn c.sub.i represents the sign of c.sub.i having a value of -1, 0 or +1. In the case of equation (5), a leak proportional to c.sub.i is provided, and a constant value of the leak, regardless of c.sub.i, is provided in the case of equation (6).
As described above, the method of avoiding the divergence by providing a leak to the tap gain correction control is already known, but it has the following problem.
As the leak (.beta. in equation (5) or l in equation (6)) becomes larger and larger, the tap gain {c.sub.i } is strongly pulled back to 0 thereby preventing {c.sub.i } from growing as a whole. In other words, the divergence of {c.sub.i } can be avoided. However, this means that {c.sub.i } can never reach {c.sub.i }.sub.opt. In the case of equation (5), the converged value {c.sub.i }.sub..infin. of {c.sub.I } is given by ##EQU4## Because {c.sub.i }.sub..infin. cannot reach {c.sub.i }.sub.opt, the residual distortion at the output of the automatic equalizer (or the remaining ghost in the case of the ghost canceller) increases naturally. The leak must be made as small as possible to reduce the residual distortion to the greatest extent, but the control diverges when the leak is too small. The value of leak enough to avoid the divergence depends upon the magnitude of a distortion in an input signal. Therefore, the value of leak must be previously set relatively large enough to meet any input signal. As a result, a leak larger than is needed would be added when the distortion of input signal is small so that the distortion cannot be reduced to a desirable extent. A system of adding a constant leak when the sum of the absolute values of the tap gains exceeds a certain value is also disclosed in Japanese laid-open patent application No. 57/185727, but it cannot add an optimum leak to meet any distortion in the input signal.